Method and apparatus for managing access to a memory

ABSTRACT

A method and apparatus for managing access to a memory of a computing system. A controller transforms a plurality of operations that represent a computing job into an operational memory layout that reduces a size of a selected portion of the memory that needs to be accessed to perform the computing job. The controller stores the operational memory layout in a plurality of memory cells within the selected portion of the memory. The controller controls a sequence by which a processor in the computing system accesses the memory to perform the computing job using the operational memory layout. The operational memory layout reduces an amount of energy consumed by the processor to perform the computing job.

CROSS-REFERENCE TO RELATED APPLICATION

This application is related to the following U.S. patent applicationentitled: “Processor-in-Memory-and-Storage Architecture,” U.S. Ser. No.______, attorney docket number SD13081, filed even date hereof, andincorporated herein by reference in its entirety.

GOVERNMENT LICENSE RIGHTS

This invention was made with United States Government support underContract No. DE-AC04-94AL85000 between Sandia Corporation and the UnitedStates Department of Energy. The United States Government has certainrights in this invention.

BACKGROUND INFORMATION

1. Field

The present disclosure relates generally to a computing system. Moreparticularly, the present disclosure relates to method and apparatus forimproving the energy efficiency of a computing system by mitigating dataerrors and memory address errors and by recycling energy.

2. Background

Reliability and energy efficiency have been and continue to be importantissues in computing. However, as computing systems become more and morecomplex and the number of hardware components in these computing systemsincreases, improving the energy efficiency of these computing systemswhile ensuring reliability may become more difficult than desired.

Currently, the increase in the number of components per square inch ofan integrated circuit over time may be approximated by Moore's Law.Moore's law is an observation that the number of transistors per squareinch of integrated circuits has approximately doubled every few years.Moore's law projects that this trend will continue for the next fewdecades.

Based on Moore's law, the power or energy dissipated per transistorshould decrease by approximately half every few years to avoidoverheating. However, reducing the power or energy in the signals usedby computing systems may eventually create reliability concerns. Forexample, reducing transistor power may eventually result in signals thatare too weak to reliably define the intended values of binary digits.Consequently, the data generated by and processed by computing systemsusing lower-powered transistors may be more error-prone.

Higher-powered transistors may be used in accordance with adiabaticprinciples to reduce these types of errors without overheating. Usingthe energy in higher-powered transistors multiple times beforedissipating the energy to the environment creates the same overalleffect as using lower-powered transistors. If the number of times energyis recycled can approximately double every few years, the doubling ofthe number of components predicted by Moore's Law could continue.Therefore, it would be desirable to have a method and apparatus thattake into account at least some of the issues discussed above, as wellas other possible issues.

SUMMARY

In one illustrative example, a method is provided for managing access toa memory of a computing system. A controller transforms a plurality ofoperations that represent a computing job into an operational memorylayout that reduces a size of a selected portion of the memory thatneeds to be accessed to perform the computing job. The controller storesthe operational memory layout in a plurality of memory cells within theselected portion of the memory. The controller controls a sequence bywhich a processor in the computing system accesses the memory to performthe computing job using the operational memory layout. The operationalmemory layout reduces an amount of energy consumed by the processor toperform the computing job.

In another illustrative example, an apparatus comprises a memory, aprocessor, and a controller that is communication with the memory andthe processor. The controller transforms a plurality of operations thatrepresent a computing job into an operational memory layout that reducesa size of a selected portion of the memory that needs to be accessed toperform the computing job. The controller stores the operational memorylayout in a plurality of memory cells within the selected portion of thememory. The controller controls a sequence by which the processoraccesses the memory to perform the computing job using the operationalmemory layout. The operational memory layout reduces an amount of energyconsumed by the processor to perform the computing job.

In yet another illustrative embodiment, a method is provided formanaging access to an adiabatic memory circuit. A controller transformsa plurality of operations that represent a computing job into anoperational memory layout that reduces a size of a selected portion of amemory array in the adiabatic memory circuit that needs to be accessedto perform the computing job. The controller stores the operationalmemory layout in a plurality of memory cells within the selected portionof the memory array. The controller controls a sequence by which aprocessor in a computing system accesses the memory array in theadiabatic memory circuit to perform the computing job using theoperational memory layout. The operational memory layout reduces anamount of energy consumed by the processor to perform the computing job.

The features and functions can be achieved independently in variousembodiments of the present disclosure or may be combined in yet otherembodiments in which further details can be seen with reference to thefollowing description and drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

The novel features believed characteristic of the illustrativeembodiments are set forth in the appended claims. The illustrativeembodiments, however, as well as a preferred mode of use, furtherobjectives and features thereof, will best be understood by reference tothe following detailed description of an illustrative embodiment of thepresent disclosure when read in conjunction with the accompanyingdrawings, wherein:

FIG. 1 is an illustration of a block diagram of a computing system inaccordance with an illustrative embodiment;

FIG. 2 is an illustration of a block diagram of a processor, a memory,and a code analysis system in accordance with an illustrativeembodiment;

FIG. 3 is an illustration of a block diagram of a memory in accordancewith an illustrative embodiment;

FIG. 4 is an illustration of a processor-in-memory-and-storagearchitecture in accordance with an illustrative embodiment;

FIG. 5 is an illustration of an adiabatic memory circuit in accordancewith an illustrative embodiment;

FIG. 6 is an illustration of a controller in the form of a block diagramin accordance with an illustrative embodiment;

FIG. 7 is an illustration of a dependency graph in accordance with anillustrative embodiment;

FIG. 8 is an illustration a two-dimensional layout in accordance with anillustrative embodiment;

FIG. 9 is an illustration of a graph in accordance with an illustrativeembodiment;

FIG. 10 is an illustration of a portion of a memory array in accordancewith an illustrative embodiment;

FIG. 11 is an illustration of a table defining various instruction codesin accordance with an illustrative embodiment;

FIG. 12 is an illustration of a process for performing reliablegeneral-purpose computing in the form of a flowchart in accordance withan illustrative embodiment;

FIG. 13 an illustration of a process for performing error mitigation inthe form of a flowchart in accordance with an illustrative embodiment;

FIG. 14 an illustration of a process for recycling energy in the form ofa flowchart in accordance with an illustrative embodiment;

FIG. 15 is an illustration of a process for managing access to a memoryin the form of a flowchart in accordance with an illustrativeembodiment; and

FIG. 16 is an illustration of a process for managing access to a memoryin the form of a flowchart in accordance with an illustrativeembodiment.

DETAILED DESCRIPTION

The illustrative embodiments recognize and take into account differentconsiderations. For example, the illustrative embodiments recognize andtake into account that it may be desirable to have a computing systemthat is both energy efficient and reliable. In particular, theillustrative embodiments recognize and take into account that errormitigation and energy recycling may be used to improve the energyefficiency and reliability of a computing system.

The illustrative embodiments recognize and take into account that errormitigation may be used to improve the reliability of a computing systemthat may be prone to data errors and memory address errors due tolower-powered transistors. In one illustrative example, a redundantresidue number system (RRNS) may be used to mitigate errors in data anderrors in memory addresses.

Further, the illustrative embodiments recognize and take into accountthat energy recycling may be used to improve the energy efficiency ofmemory in computing systems. In particular, storing energy and recyclingenergy to form a dynamic power supply that drives the memory of acomputing system in an adiabatic manner may reduce energy consumption.

In this manner, error mitigation, energy recycling, or a combination ofboth may be used to create a computing system that is bothenergy-efficient and reliable. Thus, the illustrative embodimentsprovide a method and apparatus for performing reliable, general-purposecomputing in an energy-efficient manner.

In one illustrative example, a computing system comprises a processor, amemory in communication with the processor, and a code analysis systemin communication with the processor and the memory. The processor iscomprised of a set of processor cores. A processor core in the set ofprocessor cores comprises a plurality of sub-cores in which a numericrange of each of the plurality of sub-cores is less than a total numericrange of the processor core. The code analysis system is incommunication with the processor and the memory. The code analysissystem comprises a set of code analyzers in communication with the setof processor cores. Each code analyzer performs data error detection fordata processed by a corresponding processor core of the set of processorcores and performs memory address validation for the correspondingprocessor core.

In some illustrative examples, a memory, such as the memory describedabove, may take the form of an adiabatic memory circuit. For example,the memory may comprise a memory array, a switch, and an energy storageunit. The memory array comprises a plurality of rows and a plurality ofcolumns. The switch electrically connects to a particular row of theplurality of rows of the memory array per cycle. The energy storage unitis electrically connected to the memory array through the switch. Thememory array, the switch, and the energy storage unit form an adiabaticmemory circuit that reduces heat loss through energy recycling.

In still yet another example, a method is provided for performingreliable general-purpose computing. Each sub-core of a plurality ofsub-cores of a processor core processes a same instruction at a sametime. A code analyzer receives a plurality of residues that represent acode word corresponding to the instruction and an indication of whetherthe code word is a memory address code or a data code from the pluralityof sub-cores. The code analyzer determines whether the plurality ofresidues are consistent or inconsistent. The code analyzer and theplurality of sub-cores perform a set of operations based on whether thecode word is a memory address code or a data code and based on adetermination of whether the plurality of residues are consistent orinconsistent.

Referring now to the figures and, in particular, with reference to FIG.1, an illustration of a block diagram of a computing system is depictedin accordance with an illustrative embodiment. In this illustrativeexample, computing system 100 may be used to form general-purposecomputing. In some illustrative examples, computing system 100 may bereferred to as a computing system architecture.

In one illustrative example, computing system 100 takes the form ofprocessor-in-memory-and-storage architecture 101.Processor-in-memory-and-storage architecture 101 may be implemented inthe form of integrated circuit 102. As depicted,processor-in-memory-and-storage architecture 101 includes base 104,processor 106, memory 108, and code analysis system 110.

Base 104 may be a substrate comprised of one or more layers depending onthe implementation. In one illustrative example, base 104 may comprise asingle layer of semiconductor material, such as, but not limited to,silicon. In another illustrative example, base 104 may include aninsulator layer and a semiconductor layer. The insulator layer may becomprised of, for example, without limitation, silicon oxide, aluminumoxide, fiberglass, or some combination thereof. The semiconductor layermay be comprised of one or more semiconductor materials on top of theinsulator layer. The semiconductor layer may be a thin, continuous layerover the insulator layer or a thin, discontinuous layer over theinsulator layer. In some illustrative examples, base 104 may take theform of a circuit board.

Processor 106 may be fabricated on base 104. Processor 106 may includeset of processor cores 112. As used herein, a “set of” items may includeone or more items. In this manner, set of processor cores 112 mayinclude one or more processor cores. For example, set of processor cores112 may include a single processor core or a plurality of processorcores. Each processor core of set of processor cores 112 may includemultiple sub-cores.

Processor core 114 may be an example of one of set of processor cores112. Processor core 114 may have total numeric range 116. Total numericrange 116 is the number of different numerical values that can berepresented by the hardware of processor 106. Total numeric range 116may be, for example, without limitation, 2 to the power of 32, which isequal to 4,294,967,296. In other illustrative examples, total numericrange 116 may be some other numeric range.

Processor core 114 may be formed by plurality of sub-cores 118. Each ofplurality of sub-cores 118 may have a numeric range selected such thatthe product of all of these numeric ranges equals total numeric range116. As used herein, when a sub-core of a processor core is referred toas having a numeric range, the numeric range is a property of thesub-core that indicates the number of different numerical values thatcan be represented by the sub-core. This numeric range may be based onthe number of bits that a sub-core can use to express a largestnumerical value. The number of bits that a sub-core or a processor corecan use to express a largest numerical value may be referred to as aword size.

For example, a sub-core may have a word size of 8 bits, which mayindicate that the sub-core may have a maximum numeric range of up to 2to the power of 8, which is 256. In some cases, a particular sub-coremay be configured to have a numeric range less than the maximum numericrange. For example, a particular sub-core may have a maximum numericrange of 256 but may be configured to have a numeric range of 199.

In one illustrative example, each sub-core of plurality of sub-cores 118may have numeric ranges that are byte-representable fractions of totalnumeric range 116. As one illustrative example, total numeric range 116may be slightly more than 2 to the power of 31, which is 2,149,852,322.In this example, plurality of sub-cores 118 may include 4 sub-cores.Each of these 4 sub-cores may have a numeric range that is slightly lessthan the expressible range of a byte. For example, the 4 sub-cores mayhave the numeric ranges of 199, 233, 194, and 194. In this example,these 4 sub-cores may form processor core 114 having total numeric range116 that is a product of all of these numeric ranges. For example, totalnumeric range 116 may be the product of 199, 233, 194, and 194, which is2,149,852,322.

In other illustrative examples, the numeric ranges for plurality ofsub-cores 118 may take on values that are relatively prime to eachother. In some cases, these relatively prime values may be chosen to beefficiently representable in convenient numbers of bits, such as 8 bits,16 bits, or some other number of bits.

Each processor core of set of processor cores 112 of processor 106 maybe implemented with a logic technology that scales signal power levelsdown with successive generations. In one illustrative example, eachprocessor core of set of processor cores 112 may be implemented usinglower-powered transistors that produce signals having lower signalpower. This type of scaling down of signal power may eventually lead toa rise in errors that will need to be managed. In other words, as thesignal power of the signals that are used to define the values of binarydigits decreases, the number of errors introduced in these resultingvalues may increase.

Code analysis system 110 enables error mitigation in a manner that doesnot increase the total amount of energy consumption. In particular, codeanalysis system 110 uses less energy to mitigate the errors introducedby the lowering of the signal power in the signals than is saved by thislowering of signal power. In this manner, code analysis system 110enables error mitigation for systems using signals of lower signal powerwithout completely undoing the energy benefits provided by the loweringof the signal power.

Code analysis system 110 may include set of code analyzers 122. Set ofcode analyzers 122 corresponds with set of processor cores 112. Inparticular, each of set of code analyzers 122 corresponds with aparticular one of set of processor cores 112. Each code analyzer may beused to analyze a code word received from the corresponding processorcore.

Code analyzer 124 may be an example of one of set of code analyzers 122.Code analyzer 124 is used to analyze code words 125 received fromprocessor core 114. In one illustrative example, code words 125 may begenerated by processor core 114 based on a redundant residue numbersystem (RRNS). For example, plurality of sub-cores 118 that make upprocessor core 114 may send residues that represent code words 125 tocode analyzer 124.

In this manner, code analyzer 124 may also be referred to as residueanalyzer 126. Residue analyzer 126 may include plurality ofresidue-interacting functions 127 that are used to analyze the residuesreceived from plurality of sub-cores 118 that make up processor core114. In particular, residue analyzer 126 analyzes the residues thatrepresent code words 125 to detect errors that may need to be corrected.

Both processor 106 and code analysis system 110 are in communicationwith memory 108. With respect to processor 106, each processor core ofset of processor cores 112 may be capable of communicating with memory108. Memory 108 uses signals of sufficiently high power to ensurereliability. In one illustrative example, memory 108 is implemented in amanner that allows energy recycling, to thereby improve the energyefficiency of processor-in-memory-and-storage architecture 101.

In some illustrative examples, a portion of memory 108 may usenon-volatile or persistent memory cells to retain data in the absence ofpower. Memory 108 is described in greater detail in FIG. 3 below.

Depending on the implementation, a computing system may include anynumber of duplicate blocks of processor-in-memory-and-storagearchitecture 101 on a same chip. As one illustrative example, two totens to hundreds of layers of processor-in-memory-and-storagearchitecture 101 may be fabricated on a silicon chip to form anenergy-efficient computing system.

With reference now to FIG. 2, an illustration of a block diagram ofprocessor 106, memory 108, and code analysis system 110 from FIG. 1 isdepicted in greater detail in accordance with an illustrativeembodiment. As described above, processor 106 includes set of processorcores 112. Processor core 114 of set of processor cores 112 includesplurality of sub-cores 118.

As described above, each sub-core of plurality of sub-cores 118 mayprocess data having a numeric range that is a fraction of total numericrange 116 for the data that can be processed by processor core 114formed by plurality of sub-cores 118. As one illustrative example,processor core 114 may be selected to have total numeric range 116 of2,149,852,322.

Processor core 114 may be formed using base sub-cores 202 and additionalsub-cores 204, which together form plurality of sub-cores 118.Additional sub-cores 204 may provide redundancy, which may be useful forperforming error detection. The number of additional sub-cores 204 maydetermine the number of errors that can be detected and the number oferrors that can be corrected.

For example, without limitation, processor core 114 having total numericrange 116 of 2,149,852,322 bits may be formed using 4 base sub-coreswith the numeric ranges of 199, 233, 194, and 239 and 2 additionalsub-cores with the numeric ranges of 251 and 509. All six of thesenumeric ranges are relatively prime with respect to each other. Each ofthe four base sub-cores and one of the additional sub-cores may havenumeric ranges that can be fully expressed using eight bits. The otheradditional sub-core may have a numeric range that can be fully expressedin nine bits. The two additional sub-cores may be used for performingerror detection. With two additional sub-cores, up to two errors may bedetected and one error corrected.

Sub-core 206 may be an example of one of plurality of sub-cores 118.Each of plurality of sub-cores 118 may be implemented in a mannersimilar to sub-core 206. Sub-core 206 comprises datapath 208 and controlunit 210. In some cases, sub-core 206 also includes cache 212.

Datapath 208 may be used to process the data generated by plurality ofsub-cores 118. In one illustrative example, datapath 208 may process thedata in the redundant residue number system (RRNS) representation.

Datapath 208 may be implemented in different ways. In one illustrativeexample, datapath 208 may be implemented as set of arithmetic logicunits 214. Each arithmetic logic unit (ALU) of set of arithmetic logicunits 214 may be capable of performing arithmetic and bitwise logicaloperations on integer binary numbers. In one illustrative example, setof arithmetic logic units 214 is configured to perform modulararithmetic based on a unique modulus. In this manner, each sub-core ofplurality of sub-cores 118 may be considered as performing modulararithmetic based on a unique modulus.

In one illustrative example, each base sub-core of base sub-cores 202 isselected to have a unique modulus. When additional sub-cores 204includes two additional sub-cores, the first additional sub-core mayhave a unique modulus that is greater than the various moduli of basesub-cores 202. In this illustrative example, the other additionalsub-core may have a modulus that is at least double the modulus of thefirst additional sub-core. All of the moduli of the various sub-coresmay be selected such that the moduli are relatively prime.

Each sub-core of plurality of sub-cores 118 is configured to execute thesame sequence of instructions. In particular, when no errors arepresent, each of plurality of sub-cores 118 executes exactly the sameinstruction on every clock cycle.

For example, each processor core in set of processor cores 112 mayexecute a same sequence of primary instructions in a synchronizedmanner. However, each of these primary instructions may reference a setof secondary instructions.

For example, each processor core in set of processor cores 112 mayexecute a same primary instruction. However, this primary instructionmay reference an independent secondary instruction for each processorcore. In this manner, each processor core may execute the same primaryinstruction but an independent secondary instruction that may be thesame as or different from the secondary instructions executed by theother processor cores. In particular, each sub-core of a particularprocessor core, such as processor core 114, executes the same secondaryinstruction corresponding to that processor core at the same time. Inthis manner, each processor core of set of processor cores 112 may becapable of processing different types of data based on the secondaryinstructions, while executing a same single sequence of primaryinstructions.

The various sub-cores of the various processor cores of set of processorcores 112 may output residues based on the redundant residue numbersystem (RRNS). For example, for each word of data processed, pluralityof sub-cores 118 of processor core 114 outputs plurality of residues 216that represent code word 218. More specifically, each of plurality ofresidues 216 at least partially represents code word 218. Code word 218may take the form of data code 220 or memory address code 222.

In one illustrative example, each sub-core of plurality of sub-cores 118executes one instruction, which is a secondary instruction, at a timeper instruction cycle. For example, at the beginning of an instructioncycle, sub-core 206 fetches an instruction from a particular memoryaddress in memory 108. Sub-core 206 then decodes the instruction andexecutes the instruction.

When the instruction is a memory instruction for accessing a memoryaddress that is to be read from or written to, code word 218 that isoutput from plurality of sub-cores 118 takes the form of memory addresscode 222. In this manner, plurality of sub-cores 118 output plurality ofresidues 216 that represent memory address code 222.

When the instruction is for processing data, code word 218 that isoutput from plurality of sub-cores 118 is data code 220. In this manner,plurality of sub-cores 118 output plurality of residues 216 thatrepresent data code 220.

Code analysis system 110 is in communication with processor 106 andmemory 108. Code analyzer 124 may correspond to processor core 114. Codeanalyzer 124 receives plurality of residues 216 from plurality ofsub-cores 118 of processor core 114 and analyzes plurality of residues216. Code analyzer 124 may also receive indication 224 from plurality ofsub-cores 118. Indication 224 indicates whether plurality of residues216 represent data code 220 or memory address code 222.

In particular, code analyzer 124 may use plurality ofresidue-interacting functions 127 to perform error mitigation. Forexample, code analyzer 124 analyzes plurality of residues 216 todetermine whether the residues in plurality of residues 216 areconsistent or inconsistent and to control the execution of conditionalbranches by plurality of sub-cores 118. Plurality of residues 216 may beconsidered consistent when each residue of plurality of residues 216 canbe independently traced back to the same code word. However, if at leastone residue of plurality of residues 216 is traced back to a differentcode word, then plurality of residues 216 are considered inconsistent.Any combination of tables, algorithms, equations, or formulas may beused to trace each of plurality of residues 216 back to a code word.

Regardless of whether plurality of residues 216 represent data code 220or memory address code 222, when code analyzer 124 determines thatplurality of residues 216 are inconsistent, code analyzer 124 sendsinconsistent result 226 to plurality of sub-cores 118. Plurality ofsub-cores 118 may then attempt to correct the error and resend a newplurality of residues to code analyzer 124.

For example, when plurality of residues 216 are inconsistent andplurality of residues 216 are intended to represent data code 220,plurality of sub-cores 118 may perform the necessary computations togenerate a new plurality of residues that represent data code 220. Inone illustrative example, plurality of sub-cores 118 may include sixsub-cores. When an inconsistency is found in the residue received fromone of the six sub-cores, the five correctly operating sub-cores maysave their current state to memory 108. These five sub-cores may thenrecreate their state for the sixth incorrectly operating sub-core usingthe error correction capabilities of the redundant residue numbersystem. With these six new states now saved, plurality of sub-cores 118may restart and resume operation from a repaired state.

When plurality of residues 216 are inconsistent and plurality ofresidues 216 are supposed to represent memory address code 222,plurality of sub-cores 118 may perform the necessary steps to generate anew plurality of residues that represent memory address code 222. Thissequence of residue consistency checking and error correction may beperformed a repeated number of times until plurality of residues 216 areidentified as consistent.

When code analyzer 124 makes a determination that plurality of residues216 are consistent and plurality of residues 216 represent memoryaddress code 222, code analyzer 124 then accesses the memory addressrepresented by memory address code 222. In particular, code analyzer 124generates a proper memory address based on plurality of residues 216 foruse in accessing memory 108. In one illustrative example, this memoryaddress is generated using high-power transistors that are not subjectto error. In some cases, the memory address may be in the binaryencoding of typically used memories rather than in a residue numbersystem format. The data accessed from this memory address in memory 108is then sent to plurality of sub-cores 118 for processing.

When code analyzer 124 makes a determination that plurality of residues216 are consistent and plurality of residues 216 represent data code220, code analyzer 124 generates consistent result 228 and performscondition test 230. Condition test 230 may be a test for determiningwhether data code 220 represented by plurality of residues 216 meetscondition 232 or not. In one illustrative example, condition 232 may bethat data code 220 is non-negative, that data code 220 is negative, orsome other type of condition.

The result of condition test 230 may be test result 234. Test result 234may be either true or false. For example, without limitation, whencondition 232 is that data code 220 is negative, test result 234 may betrue when data code 220 is negative and false when data code 220 ispositive or zero.

Code analyzer 124 sends test result 234 and consistent result 228 toplurality of sub-cores 118. Plurality of sub-cores 118 may use testresult 234 to determine the next instruction to be fetched, decoded, andexecuted. For example, plurality of sub-cores 118 may all conditionallybranch, or jump, to a new instruction based on test result 234 or mayproceed to a next instruction in the current sequence of instructionsbased on test result 234. In some cases, plurality of sub-cores 118 mayignore the test result when executing non-conditional instructions.

In this manner, code analyzer 124 may be used to perform errormitigation for processor core 114. In particular, code analyzer 124 mayperform detection of errors in the data processed by plurality ofsub-cores 118 and may perform memory address validation for processorcore 114. Similarly, each code analyzer of set of code analyzers 122 maybe used to mitigate errors in the data processed by the sub-cores thatform each corresponding processor core of set of processor cores 112,respectively.

Plurality of residues 216 may be conveyed between processor 106 andmemory 108 in a straightforward manner. The redundant residues of theredundant residue number system in processor core 114 of processor 106protect the data stored in memory 108.

Validating a memory address may be important to protecting the datastored in memory. For example, a write operation to an incorrect memoryaddress in memory 108 may result in important data being overwritten. Anerror in the memory address for a read operation from that memoryaddress may result in computational errors.

With reference now to FIG. 3, an illustration of a block diagram ofmemory 108 from FIG. 1 is depicted in accordance with an illustrativeembodiment. In one illustrative example, memory 108 takes the form ofadiabatic memory circuit 300. Adiabatic memory circuit 300 includesplurality of memory arrays 301, switch system 302, and energy storageunit 304.

Memory array 306 may be an example of one of plurality of memory arrays301. Memory array 306 may also be referred to as a memory bank. Asdepicted, memory array 306 may be defined as comprising plurality ofrows 308 and plurality of columns 310.

Switch system 302 may include any number of switches. In oneillustrative example, switch system 302 includes a different switch foreach of plurality of memory arrays 301. A switch corresponding to aparticular memory array may electrically connect to only one row of thatcorresponding memory array per cycle.

As one illustrative example, switch system 302 may include switch 312that corresponds to memory array 306. Switch 312 electrically connectsto one particular row of plurality of rows 308 of memory array 306 percycle. Switch 312 may be bi-directional in that switch 312 allows abi-directional flow of energy through switch 312.

Energy storage unit 304 may be electrically connected to plurality ofmemory arrays 301 through switch system 302. For example, energy storageunit 304 may be electrically connected to switch system 302.

In one illustrative example, energy storage unit 304 may be implementedas inductor 314. Inductor 314 may be electrically connected to combinedeffective capacitances 316 of plurality of memory arrays 301 throughswitch system 302.

As one illustrative example, at a given point in time, switch 312 may beconnected to particular row 318 of memory array 306. Inductor 314 iselectrically connected to switch 312 such that inductor 314 may beconsidered electrically connected to effective capacitance 320 betweenparticular row 318 of memory array 306 and ground. Combined effectivecapacitances 316 may be the sum of the effective capacitancescorresponding to the particular row in each of plurality of memoryarrays 301 to which switch system 302 connects at a given point in time.In other words, combined effective capacitances 320 may be the sum of aneffective capacitance for each memory array of plurality of memoryarrays 301.

By connecting to combined effective capacitances 316 in this manner,inductor 314 may reduce heat loss. In particular, the amount of heatlost to the surroundings may be reduced and a higher percentage ofenergy may be recycled. Inductor 314 may be used to recycle the energyfrom combined effective capacitances 316 back onto plurality of memoryarrays 301 through switch system 302.

This type of energy recycling in memory 108 improves the energyefficiency of computing system 100 in FIG. 1. Further, the errormitigation capabilities provided by using code analysis system 110 asdescribed in FIG. 2 may allow processor 106 to be implemented usinglower signal power. Together, the energy recycling associated withmemory 108 and the error mitigation associated with code analysis system110 may improve the overall energy efficiency of computing system 100 inFIG. 1 without sacrificing the reliability of computing system 100.

The illustrations of computing system 100 in FIG. 1, processor 106,memory 108, and code analysis system 110 in FIGS. 1-2, and adiabaticmemory circuit 300 in FIG. 3 are not meant to imply physical orarchitectural limitations to the manner in which an illustrativeembodiment may be implemented. Other components in addition to or inplace of the ones illustrated may be used. Some components may beoptional. Also, the blocks are presented to illustrate some functionalcomponents. One or more of these blocks may be combined, divided, orcombined and divided into different blocks when implemented in anillustrative embodiment.

With reference now to FIG. 4, an illustration of aprocessor-in-memory-and-storage architecture is depicted in accordancewith an illustrative embodiment. In this illustrative example,processor-in-memory-and storage architecture 400 may be an example ofone implementation for processor-in-memory-and-storage architecture 101in FIG. 1.

In this illustrative example, processor-in-memory-and storagearchitecture 400 is implemented on base 402. Base 402 may be an exampleof one implementation for base 104 in FIG. 1. As depicted, base 402 ispositioned over heat sink 410.

Processor-in-memory-and storage architecture 400 includes processor 404,interconnects 406, and memory and storage layers 408. Processor 404 maybe an example of one implementation for processor 106 in FIGS. 1 and 2.Interconnects 406 connect processor 404 to memory and storage layers408. Memory and storage layers 408 may be an example of oneimplementation for memory 108 in FIG. 1. Processor-in-memory-and storagearchitecture 400 may be replicated any number of times and stacked inlayers over a single base 402 or over multiple modules interconnected bywires or conductive traces on a circuit board, thus forming a morecomplex computing system.

With reference now to FIG. 5, an illustration of an adiabatic memorycircuit is depicted in accordance with an illustrative embodiment. Inthis illustrative example, adiabatic memory circuit 500 may be anexample of one implementation for adiabatic memory circuit 300 in FIG.3.

As depicted, adiabatic memory circuit 500 includes plurality of memoryarrays 502, switch system 504, and energy storage unit 506. Energystorage unit 506 is an example of one implementation for energy storageunit 304 in FIG. 3. In this illustrative example, energy storage unit506 is implemented as an inductor.

Plurality of memory arrays 502 include memory array 508, memory array510, memory array 512, and memory array 514. Each of these memory arrayscomprises a plurality of rows and a plurality of columns. Each ofplurality of memory arrays 502 may be an example of one implementationfor memory array 306 in FIG. 3.

In this illustrative example, switch system 504 is implemented usingcircuit switching, such as with one or more microelectromechanicalsystems (MEMs) devices, pass transistors, or other suitable types oftechnologies. As depicted, switch system 504 may include switch 516,switch 518, switch 520, and switch 522. Each of these switches may be anexample of one implementation for switch 312 in FIG. 3. Switch 516,switch 518, switch 520, and switch 522 correspond to memory array 508,memory array 510, memory array 512, and memory array 514, respectively.

Each switch in switch system 504 electrically connects to one row of thecorresponding memory array at a time and is capable of allowing energyto flow in both directions between energy storage unit 506 and thecorresponding memory array with reduced heat loss. For example, switch516 electrically connects to one row of memory array 508 at a time andallows a bi-directional flow of energy through switch 516 between energystorage unit 506 and memory array 508 with reduced heat loss.

Energy storage unit 506 electrically connects in series to the sum ofeffective capacitance 524, effective capacitance 526, effectivecapacitance 528, and effective capacitance 530. This sum may be referredto as the combined effective capacitances over plurality of memoryarrays 502. As depicted, energy storage unit 506 electrically connectsin series to effective capacitance 524 between particular row 532 towhich switch 516 is connected and ground. Energy storage unit 506electrically connects in series to the effective capacitance for eachmemory array of plurality of memory arrays.

Connecting energy storage unit 506 to plurality of memory arrays 502through switch system 504 in the manner described above increases theamount of energy that is recycled back onto plurality of memory arrays502. Increasing the recycled energy improves the overall energyefficiency of the computing system within which adiabatic memory circuit500 is used.

With reference now to FIG. 6, an illustration of a controller isdepicted in the form of a block diagram in accordance with anillustrative embodiment. In this illustrative example, controller 600may be implemented using hardware, firmware, software, or a combinationthereof.

For example, controller 600 may be implemented within computing system100 from FIG. 1. In some cases, controller 600 may be implemented usinga microprocessor or some other type of processor unit that is incommunication with processor 106 and memory 108 of computing system 100from FIG. 1. In other illustrative examples, controller 600 may beimplemented as part of processor 106. For example, controller 600 may beimplemented using one or more processor cores that make up processor 106from FIG. 1.

Controller 600 is used to optimize the portion of a memory that is usedto store computing job 602. As one illustrative example, by optimizingthe portion of memory 108 from FIG. 1 that is used to store computingjob 602, the amount of energy 604 consumed by processor 106 from FIG. 1during the accessing of memory 108 to perform computing job 602 may bereduced. Computing job 602 may be some type of special-purpose orgeneral-purpose computing job.

As depicted, controller 600 identifies plurality of operations 606 thatrepresent computing job 602. In one illustrative example, plurality ofoperations 606 includes plurality of sparse matrix operations 608 thatare generated using sparse matrix theory. In some cases, plurality ofoperations 606 may also include set of additional operations 610. Inthis manner, controller 600 may express computing job 602 usingplurality of sparse matrix operations 608 and set of additionaloperations 610.

Plurality of sparse matrix operations 608 may include, for example,without limitation, sparse vector-matrix multiplication operations thatare all performed using selected sparse matrix 612. Selected sparsematrix 612 may also be referred to as a fundamental sparse matrix.

Selected sparse matrix 612 has a defined sparsity pattern. This sparsitypattern is the particular locations within selected sparse matrix 612having numerical values that are zero and numerical values that arenonzero. Selected sparse matrix 612 also includes specific values forthe nonzero numerical values. Plurality of sparse matrix operations 608may include a vector-matrix multiply operation, which is an operationthat uses but does not change either the sparsity pattern or thenumerical values of selected sparse matrix 612.

However, other types of sparse matrix operations, such as a learningoperation in a neural network, may change one or more numerical valuesof selected sparse matrix 612 but leave the sparsity pattern of selectedsparse matrix 612 unchanged. An operation that changes the sparsitypattern of a sparse matrix may be handled as an additional operation,such as one of set of additional operations 610.

In one illustrative example, the output values produced for outputvector 616 for a current sparse matrix operation may be used as theinput values for input vector 614 for a next sparse matrix operation. Inother illustrative examples, set of additional operations 610 mayinclude an operation that modifies the output values produced for outputvector 616 for a current sparse matrix operation to form modified outputvalues. These modified output values may then be used as the inputvalues for input vector 614 for a next sparse matrix operation.

Controller 600 generates initial layout 618 that includes arepresentation of selected sparse matrix 612. In some illustrativeexamples, initial layout 618 may also include a representation of inputvector 614, output vector 616, or both.

In one illustrative example, initial layout 618 takes the form of,without limitation, sparse dependency graph 620. In some illustrativeexamples, sparse dependency graph 620 is a sparse, directed acyclicgraph (DAG) of arithmetic operations. In one illustrative example,initial layout 618 lays out the data dependencies and data movementsassociated with performing a multiplication of input vector 614 byselected sparse matrix 612 to yield output vector 616.

Controller 600 transforms initial layout 618 into operational memorylayout 622. In particular, controller 600 converts initial layout 618into operational memory layout 622 that reduces a size of selectedportion 624 of memory 108 that needs to be accessed by processor 106 toperform computing job 602. This transformation may be performed usingone or more different types of graph layout algorithms or combinationthereof. Operational memory layout 622 is a compressed representation ofinitial layout 618 that represents all data operations and data movementin a top-down manner. In particular, operational memory layout 622 issmaller in size than initial layout 618.

In one illustrative example, controller 600 forms operational memorylayout 622 using two-dimensional layout 626 of nodes. For example,controller 600 may transform each sparse matrix operation of pluralityof sparse matrix operations 608 into plurality of nodes 628. Pluralityof nodes 628 may include set of input nodes 630, set of matrix elementnodes 632, and set of output nodes 634. Further, each of plurality ofnodes 628 includes numerical value 636, instruction code 638, or both.

Each of set of input nodes 630 may represent an input value of inputvector 614. This input value is a numerical value. Each of set of outputnodes 634 may represent an output value of output vector 616. Thisoutput value is a numerical value.

Further, each matrix element node of set of matrix element nodes 632 mayrepresent a matrix element of selected sparse matrix 612. This matrixelement includes a numerical value. Additionally, each matrix elementnode of set of matrix element nodes 632 may correspond to a set ofarithmetic operations, which may include at least one of an additionoperation or a multiplication operation. This set of arithmeticoperations may be defined by an instruction code. In some illustrativeexamples, an instruction code may also specify data movement operationsthat do not change numerical values. For example, data movementoperations include, but are not limited to, delaying a numerical valueby a time step, sending a numerical value from a particular processorcore to another processor core to the left or right of the particularprocessor core. In this manner, each matrix element node of set ofmatrix element nodes 632 includes a numerical value and an instructioncode.

Controller 600 arranges set of input nodes 630, set of matrix elementnodes 632, and set of output nodes 634 that form plurality of nodes 628to form two-dimensional layout 626. Two-dimensional layout 626 is usedto form operational memory layout 622. Depending on the implementation,operational memory layout 622 may include all of two-dimensional layout626, only the portion of two-dimensional layout 626 that includes set ofmatrix element nodes 632, or some other portion of two-dimensionallayout 626.

In one illustrative example, controller 600 stores set of matrix elementnodes 632 in plurality of memory cells 636 within selected portion 624of memory 108 based on operational memory layout 622. In this manner, anumerical value and an instruction code are stored in each of pluralityof memory cells 636. Operational memory layout 622 may span plurality ofmemory rows 640 within memory 108. In this illustrative example,controller 600 stores set of input nodes 630, set of output nodes 634,or both into registers associated with processor 106.

Controller 600 determines sequence 642 by which memory rows of memory108 need to be accessed to perform computing job 602. Sequence 642 mayinclude, for example, without limitation, a plurality of cycles ofaccessing plurality of memory rows 640. In some cases, a particularcycle may include accessing one or more additional memory rows of memory108. In this manner, the memory rows accessed during each cycle ofmemory access may be the same or different.

As one illustrative example, controller 600 determines that processor106 is to access selected group of memory rows 644 in memory 108.Selected group of memory rows 644 includes at least plurality of memoryrows 640. Processor 106 accesses selected group of memory rows 644 inmemory 108 according to sequence 642 determined by controller 600.

For example, during one cycle, processor 106 may access each memory rowin selected group of memory rows 644 of memory 108 according to sequence642. Processor 106 reads each memory row and implements, or executes, aset of tasks corresponding to each memory row. At the end of the cycle,processor 106 produces output values for output vector 616. These outputvalues may then be used as input values for input vector 614 at thebeginning of the next cycle, as determined by sequence 642. This processmay be repeated until sequence 642 has been completed.

When processor 106 reads a memory row that is one of plurality of memoryrows 640 corresponding to operational memory layout 622, each memorycell in a particular memory row will be read by the correspondingprocessor core of processor 106. Each processor core may use set ofinstruction code definitions 646 that have been loaded into thatprocessor core to decode the instruction code in a memory cell. Eachinstruction code definition may define one or more instructions for acorresponding instruction code.

In this manner, when a processor core accesses a particular memory celland retrieves a numerical value and an instruction code from that memorycell, the processor core uses set of instruction code definitions 646 toidentify a set of instructions represented by the instruction code. Theprocessor core then executes the set of instructions using the numericalvalue. If executing the set of instructions modifies a numerical valuefor selected sparse matrix 612, the numerical value may then be writtenback into memory 108.

When memory 108 includes adiabatic memory circuit 300 from FIG. 3,controller 600 controls switch system 302. As one illustrative example,input vector 614 may be loaded into set of processor cores 112 that formprocessor 106 such that one input value is loaded into each processorcore of set of processor cores 112.

One cycle of processing may correspond to the processing of input vector614 using selected sparse matrix 612 to form a final output vector 616.In one illustrative example, a cycle of processing corresponds to theperforming of one sparse matrix operation.

For a particular cycle of processing, controller 600 identifies selectedgroup of memory rows 644. Controller 600 then controls switch system 302of adiabatic memory circuit 300 such that switch system 302 electricallyconnects to each memory row of selected group of memory rows 644, one ata time.

When switch system 302 connects to a particular memory row, energy ismoved from energy storage unit 304 to the memory row. Set of processorcores 112 access the memory row using the energy transferred to thememory row from the energy storage unit 304 to charge the effectivecapacitance of that memory row.

Each processor core of set of processor cores 112 reads a correspondingmemory cell of the memory row and retrieves a numerical value, aninstruction code, or both. If an instruction code and a numerical valueare retrieved, a processor core executes a set of instructionsrepresented by the instruction code based on the numeric value. Theresulting value of this processing may then be moved into a registerassociated with the processor core or another processor core If only anumerical value is retrieved, the processor core may shift the numericalvalue into an input register associated with the processor core oranother processor core.

The energy is then moved from the current memory row back through theswitch and back into energy storage unit 304. In other words, the energyis recycled.

The use of operational memory layout 622 enables the energy consumed byprocessor 106 due to the accessing of memory 108 to be reduced. Further,using operational memory layout 622 in combination with adiabatic memorycircuit 300 improves the energy efficiency of computing system 100.

The illustration of controller in FIG. 6 is not meant to imply physicalor architectural limitations to the manner in which an illustrativeembodiment may be implemented. Other components in addition to or inplace of the ones illustrated may be used. Some components may beoptional. Also, the blocks are presented to illustrate some functionalcomponents. One or more of these blocks may be combined, divided, orcombined and divided into different blocks when implemented in anillustrative embodiment.

With reference now to FIG. 7, an illustration of a dependency graph isdepicted in accordance with an illustrative embodiment. In thisillustrative example, dependency graph 700 has been created based on asparse matrix operation that involves input vector 702, sparse matrix704, and output vector 706.

Input vector 702, sparse matrix 704, and output vector 706 may beexamples of implementations for input vector 614, selected sparse matrix612, and output vector 616, respectively, in FIG. 6. In thisillustrative example, dependency graph 700 represents a vector-matrixmultiplication in which input vector 702 is multiplied by sparse matrix704 to produce output vector 706.

In this illustrative example, the individual vector elements of inputvector 702 and output vector 706 and the matrix elements of sparsematrix 704 are rearranged to form dependency graph 700 having pluralityof rows 708. Input vector 702 is represented by input elements 710, 712,714, and 716 in dependency graph 700. The matrix elements of sparsematrix 704 are represented by plurality of matrix elements 718. Outputvector 706 is represented by output elements 720, 722, 724, and 726.Elements 728, 730, 732, and 734 represent the initialization of theoutput values for output vector 706. In this manner, elements 728, 730,732, and 734 may be referred to as initialized output values that forman initialized output vector.

As depicted, each of input elements 710, 712, 714, and 716 is associatedwith a numerical value. Similarly, each of output elements 720, 722,724, and 726 is associated with a numerical value. In this illustrativeexample, each matrix element of plurality of matrix elements 718 isassociated with a numerical value and represents a multiplicationoperation, an addition operation, or a combination of these twooperations.

In this illustrative example, input values, which are denoted by “x,”flow down and to the right. For example, the input value in inputelement 712 flows down and to the right, as indicated by arrows 733.Output values, which are denoted by “y,” are initialized to zero, asindicated by elements 728, 730, 732, and 734. Output values flow downand to the left but are updated along the way. For example, aninitialized output value, represented by element 732 is initialized tozero and then flows down and to the right, as indicated by arrows 735.Each time an input value, “x,” and an output value, “y,” meet at amatrix element containing a numerical value “a_(ij),” the output valueis updated to be y+a_(ij)*x.

Dependency graph 700 may be modified to form a sparse dependency graph.For example, each matrix element of plurality of matrix elements 718that has a numerical value of zero may be removed from dependency graph700. In particular, matrix elements 736, 738, 740, 742, 744, 746, 748,750, 752, and 754 may be removed from dependency graph 700 to form asparse dependency graph. The remaining matrix elements, input elements,and output elements may then be used to form an operational memorylayout, such as operational memory layout 622 in FIG. 6.

The matrix elements having numerical values of zero may be removedbecause the arithmetic operation involved is to accumulate the productsof matrix elements and vector elements. When the numerical value of amatrix element is zero, multiplying the matrix element by any valueresults in zero. The addition of zero to any accumulating sum has noeffect on the accumulating sum. Thus, the matrix elements havingnumerical values of zero may be removed due to the nature of thevector-matrix multiplication problem without affecting the final result.

In other illustrative examples, the sparse dependency graph may bedirectly created using various graph analytics and graph layoutalgorithms without having to first create dependency graph 700. Theinputs to these types of algorithms may be graphs that can berepresented as sparse matrices. The algorithms may then be used to findparameters such as, for example, without limitation, graph diameter,minimum flow, maximum flow, some other type of parameter, or somecombination thereof.

With reference now to FIG. 8, an illustration of a two-dimensionallayout is depicted in accordance with an illustrative embodiment. Inthis illustrative example, two-dimensional layout 800 may be an exampleof one implementation for two-dimensional layout 626 in FIG. 6.Two-dimensional layout 626 is generated based on dependency graph 700.In particular, the sparse dependency graph created by removing matrixelements 736, 738, 740, 742, 744, 746, 748, 750, 752, and 754 fromdependency graph 700 in FIG. 7 may be transformed into two-dimensionallayout 800.

In this illustrative example, two-dimensional layout 800 includes rows802, 804, 806, 808, and 810 and columns 812, 814, and 816. Each ofcolumns 812, 814, and 816 may correspond to a corresponding processorcore of a set of processor cores. The three columns may correspond tothree processor cores in this illustrative example.

The set of processor cores may process each of the rows oftwo-dimensional layout 800, one at a time and at a same time. Asdepicted in this example, a particular element of a row may containinformation that will be stored in memory or loaded into a register.

As depicted, two-dimensional layout 800 may be used to createoperational memory layout 817. Operational memory layout 817 includesmatrix elements 818, 820, 822, 824, 826, and 828. Operational memorylayout 817 defines the way in which information is stored in memory andthereby, the way in which the set of processor cores will performcomputations.

For example, operational memory layout 817 is fully limited to column814 and column 816. Thus, the instructions that correspond to the matrixelements of operational memory layout 817 will only be executed by theprocessor cores corresponding to these columns.

In other illustrative examples, the entirety of two-dimensional layout800 may be used as operational memory layout 817. In this manner, inputelements and output elements will be stored in memory and may need to bewritten over during processing.

With reference now to FIG. 9, an illustration of a graph in anotherformat is depicted in accordance with an illustrative embodiment. Inthis illustrative example, graph 900 directly corresponds totwo-dimensional layout 800 in FIG. 8.

As depicted, graph 900 includes columns 902, 904, and 906, whichcorrespond to columns 812, 814, and 816, respectively in FIG. 8. Graph900 includes rows 908, 910, 912, 914, and 916, which correspond to rows802, 804, 806, 808, and 810, respectively, in FIG. 8. In thisillustrative example, the various elements that make up two-dimensionallayout 800 in FIG. 8 are represented as nodes in graph 900. Arrows 918,which may also be referred to as arcs, represent the data movements andsparsity pattern of sparse matrix 704 in FIG. 7, laid out intwo-dimensions to form graph 900.

With reference now to FIG. 10, an illustration of a portion of a memoryarray is depicted in accordance with an illustrative embodiment. In thisillustrative example, portion 1000 of memory array 1001 includesplurality of memory cells 1002. As depicted, portion 1000 of memoryarray 1001 includes plurality of rows 1003 and plurality of columns1004.

Each memory cell in plurality of memory cells 1002 stores a numericalvalue and an instruction code in this illustrative example. Thenumerical values and instruction codes stored in plurality of memorycells 1002 may be based on graph 900 in FIG. 9.

As depicted, plurality of memory cells 1002 include input cells 1006,matrix element cells 1008, and output cells 1010. Input cell 1012 is anexample of one of input cells 1006. Matrix element cell 1014 is anexample of one of matrix element cells 1008. Output cell 1016 is anexample of one of output cells 1010.

As depicted, input cell 1012 includes the numerical value “x₁” and theinstruction code “IN.” Matrix element cell 1014 includes the numericalvalue “a₃₀” and the instruction code “E.” Output cell 1016 includes thenumerical value “y₃” and the instruction code “G.”

Each column of plurality of columns 1004 is processed by a differentprocessor core. Further, these processor cores process each row ofplurality of rows 1003 during a same time step. At each time step, aprocessor core will either store the resulting value of a computationthat has been performed for use at a next time step or transfer theresulting value to a neighboring processor core to the left or right ofthe processor core.

In this illustrative example, input values of an input vector for avector-matrix multiply operation may be written into memory array 1001in input cells 1006 and output values of the resulting output vector maybe written into memory array 1001 in output cells 1010. However, inother illustrative examples, input cells 1006, output cells 1010, orboth may not be needed. For example, the output values of the outputvector may be more efficiently stored in registers associated with theprocessor core if those output values are immediately used as the inputvalues of the next input vector processed.

Turning now to FIG. 11, an illustration of a table defining each of thevarious instruction codes shown in FIG. 10 is depicted in accordancewith an illustrative embodiment. In this illustrative example, table1100 contains plurality of columns 1102. Plurality of columns 1102includes instruction code column 1104, Y output column 1106, left outputcolumn 1108, right output column 1110, and wait zone output column 1112.

In table 1100,

“init” is an input value of an input vector;

“a” is a numerical value of a corresponding matrix element stored inmemory;

“Yin” is a core input, which is an initialized output value at a firsttime step or a value stored in the processor core from the output, Yout,of that processor core in the previous time step;

“Yout” is a core output, which is the output from a processor core thatwill be used as an input to the same processor core at the next timestep;

“Rin” is a right input, which is the input to a processor core that isan initialized output value at a first time step or the output from aprevious time step from another processor core to the immediate right;

“Rout” is a right output, which is the output from a processor core thatwill be used as an input to another processor core that is to theimmediate right at a next time step;

“Lin” is a left input, which is the input to a processor core that is aninitialized output value at a first time step or the output from aprevious time step from another processor core to the immediate left;

“Lout” is a left output, which is the output from a processor core thatwill be used as an input to another processor core that is to theimmediate left at a next time step;

“WZin” is a wait zone input, which is an initialized value at a firsttime step or a value from a previous time step retrieved from atemporary storage location, “wait zone,” of a processor core; and

“WZout” is a wait zone output to the temporary storage location, “waitzone,” of a processor core that will be used by the same processor coreat a next time step.

Instruction code column 1104 includes the various instruction codesdepicted in FIG. 10. Y output column 1106 defines the core outputs to beoutput from a processor core based on a corresponding instruction code.In particular, the core output may be the result of a computation to beperformed by the processor core based on the corresponding instructioncode. The processor core then uses the result of this computation itselfas an input for a computation to be performed at a next time step.

Left output column 1108 defines the left outputs for correspondinginstruction codes. Right output column 1110 defines the right outputsfor corresponding instruction codes. Wait zone output column 1112defines the wait zone outputs for corresponding instruction codes.

The instruction codes defined in table 1100 are used to perform aparticular type of operation, which is a sparse matrix operation in thisillustrative example. However, a computing job may comprise multiplesparse matrix operations and other types of operations. Depending on theimplementation, a different set of instruction code definitions may beused for each of the different types of operations.

In one illustrative example, a computer-implemented, artificial neuralnetwork may include a learning phase and an image recognition phase. Theimage recognition phase may use sparse matrix-vector multiplyoperations, while the learning phase may use an operation that altersthe sparse matrix values, because the sparse matrix values representlearned information. In this particular example, the instruction codesdefined in table 1100 would be used to perform image recognition.However, a different set of instruction codes would be used forlearning. However, the two sets of instruction codes would use the sameoperational memory layout so that the operational memory layout wouldnot need to be reloaded each time.

With reference now to FIG. 12, an illustration of a process forperforming reliable general-purpose computing is depicted in the form ofa flowchart in accordance with an illustrative embodiment. The processillustrated in FIG. 12 may be implemented using computing system 120from FIG. 1.

The process begins by processing, by each sub-core of a plurality ofsub-cores of a processor core, a same instruction at a same time(operation 1200). Next, a plurality of residues that represent a codeword corresponding to the instruction and an indication of whether thecode word is a memory address code or a data code are received by a codeanalyzer from the plurality of sub-cores (operation 1202).

A determination is made, by the code analyzer, of whether the pluralityof residues are consistent or inconsistent (operation 1204). Inoperation 1204, the consistency check is performed to ensure that all ofthe plurality of residues may be traced back to a same code word. If atleast one of the plurality of residues cannot be traced back to the samecode word as the other residues, then the plurality of residues areconsidered inconsistent.

The code analyzer and the plurality of sub-cores perform a set ofoperations based on whether the code word is a memory address code or adata code and a determination of whether the plurality of residues areconsistent or inconsistent (operation 1206), with the process thenreturning to operation 1200. Operation 1200, operation 1202, operation1204, and operation 1206 may be performed per instruction cycle of thecomputing system.

With reference now to FIG. 13, an illustration of a process forperforming error mitigation is depicted in the form of a flowchart inaccordance with an illustrative embodiment. The process illustrated inFIG. 13 may be implemented using a code analyzer, such as code analyzer144 described in FIGS. 1-2.

The process begins by receiving a plurality of residues that represent acode word from a plurality of sub-cores of a processor core and anindication of whether the code word is a memory address code or a datacode (operation 1300). Next, a determination is made as to whether theplurality of residues are consistent (operation 1302).

If the plurality of residues are not consistent, an inconsistent resultis sent to the plurality of sub-cores (operation 1304). The process thenwaits (operation 1306) until a new plurality of residues is receivedfrom the plurality of sub-cores as described above in operation 1300. Inthis illustrative example, in response to receiving the inconsistentresult sent from the code analyzer in operation 1304, the plurality ofsub-cores may attempt to correct the error and send a new plurality ofresidues back to the code analyzer.

With reference again to operation 1302, if the plurality of residues areconsistent, a first set of operations are performed if the code wordrepresented by the plurality of residues is a memory address code and asecond set of operations are performed if the code word represented bythe plurality of residues is a data code. For example, if the code wordis a memory address code, the code analyzer generates a memory addressfor accessing memory based on the plurality of residues (operation1308). The code analyzer then accesses the memory using the memoryaddress generated to cause the data stored at that memory address to besent to the plurality of sub-cores (operation 1310), with the processthen proceeding to operation 1306 described above.

With reference again to operation 1302, if the plurality of residues areconsistent and the code word represented by the plurality of residues isa data code, the code analyzer performs a condition test based on aselected condition using the plurality of residues (operation 1312). Thecode analyzer then sends a test result based on the condition test tothe plurality of sub-cores (operation 1314), with the process thenproceeding to operation 1306 described above.

In one illustrative example, the condition test performed in operation1312 may be whether the data code is a negative integer or not. If thedata code is a negative integer, then a true test result may be sent toplurality of sub-cores in operation 1314. If the data code is anon-negative integer, then a false test result may be sent to theplurality of sub-cores in operation 1314.

Based on the test result received by the plurality of sub-cores, theplurality of sub-cores may fetch, decode, and execute a nextinstruction. For example, if a true test result is received, theplurality of sub-cores may branch, or jump, to new instructionout-of-sequence with respect to the current sequence of instructionsbeing processed. If a false test result is received, the plurality ofsub-cores may fetch, decode, and execute the next instruction in thecurrent sequence of instructions being processed.

The error mitigation performed in the process described in FIG. 13 maybe used to ensure the reliability of the computations performed by theplurality of sub-cores. This process may be a simple and low-energymethod for detecting errors introduced by using signals of lower powerto define the values of binary digits.

With reference now to FIG. 14, an illustration of a process forrecycling energy is depicted in the form of a flowchart in accordancewith an illustrative embodiment. The process illustrated in FIG. 12 maybe implemented using adiabatic memory circuit 300 in FIG. 3.

The process begins moving a switch to electrically connect the switch toa particular row of a plurality of rows of a memory array such that theparticular row can be accessed for reading, writing, or both (operation1200). In one illustrative example, this memory array may be part of acomputing system, such as computing system 120 in FIG. 1. For example,the memory array may belong to a processor-in-memory-and-storagearchitecture, such as processor-in-memory-and-storage architecture 121in FIG. 1.

Energy is moved through the switch from an energy storage unit that iselectrically connected to the switch into the particular row of thememory array (operation 1202). In one illustrative example, the energystorage takes the form of an inductor. However, in other illustrativeexamples, the energy storage unit may take the form of some otherelectromechanical device capable of storing energy.

In some cases, during operation 1402, energy provided from a powersupply may also be moved into the particular row of the memory array.However, by moving energy from the energy storage unit into theparticular row of the memory array, the amount of energy drawn from thepower supply may be reduced.

As the particular row of the memory array is accessed for either readingor writing, energy is withdrawn from the particular row, moved throughthe switch, and returned to the energy storage unit (operation 1404),with the process then returning to operation 1400 described above. Inthis manner, the switch allows a bi-directional flow of energy betweenthe energy storage unit and the memory array.

The percentage of the amount of energy sent into the particular row ofthe memory array from the energy storage unit, power supply, or acombination of the two that is returned to the energy storage unitthrough the switch may be above a selected threshold. This percentagemay be referred to as the percentage of row energy recycled. In oneillustrative examples, the percentage of row energy recycled may begreater than about 95 percent. In some illustrative examples, thepercentage of row energy recycled may be greater than about 98 percent.

The process described in FIG. 14 may ultimately reduce heat loss duringaccessing of the memory array. In particular, by enabling recycling ofthe energy used to access the rows of the memory array, overall heatloss may be reduced. This type of energy recycling, and thereby heatloss reduction, may improve the overall energy efficiency of thecomputing system to which the memory array belongs.

With reference now to FIG. 15, an illustration of a process for managingaccess to a memory is depicted in the form of a flowchart in accordancewith an illustrative embodiment. The process illustrated in FIG. 15 maybe implemented using a controller, such as controller 600 in FIG. 6.

The process begins by, transforming, by a controller, a plurality ofoperations that represent a computing job into an operational memorylayout that reduces a size of a selected portion of the memory thatneeds to be accessed to perform the computing job (operation 1500).Next, the controller stores the operational memory layout in a pluralityof memory cells within the selected portion of the memory (operation1502).

Thereafter, the controls a sequence by which a processor in thecomputing system accesses the memory to perform the computing job usingthe operational memory layout in which the operational memory layoutreduces an amount of energy consumed by the processor to perform thecomputing job (operation 1504), with the process terminating thereafter.When the processor accesses the memory according to the sequence, theprocessor may access a selected group of memory rows in the memoryaccording to the sequence. The operational memory layout spans aplurality of memory rows in the memory that are included in the selectedgroup of memory rows. Further, the processor may repeat this cycle anynumber of types to perform the computing job.

With reference now to FIG. 16, an illustration of a process for managingaccess to a memory is depicted in the form of a flowchart in accordancewith an illustrative embodiment. The process illustrated in FIG. 16 maybe implemented using a controller, such as controller 600 in FIG. 6.

The process may begin by expressing a computing job using a plurality ofsparse matrix operations and a set of additional operations in which theplurality of sparse matrix operations correspond to a selected sparsematrix (operation 1600). Next, an initial layout is generated thatincludes a representation of the selected sparse matrix (operation1602).

The initial layout is transformed into the operational memory layoutsuch that the operational memory layout is smaller in size than theinitial layout and reduces a size of a selected portion of a memory thatneeds to be accessed to perform the computing job (operation 1604). Theoperational memory layout is stored in a plurality of memory cellswithin the selected portion of the memory (operation 1606). A sequenceby which a processor in the computing system accesses the memory toperform the computing job using the operational memory layout iscontrolled in which the operational memory layout enables the processorto consume less energy during accessing of the memory to perform thecomputing job (operation 1608), with the process terminating thereafter.

The flowcharts and block diagrams in the different depicted embodimentsillustrate the architecture, functionality, and operation of somepossible implementations of apparatuses and methods in an illustrativeembodiment. In this regard, each block in the flowcharts or blockdiagrams may represent a module, a segment, a function, and/or a portionof an operation or step.

In some alternative implementations of an illustrative embodiment, thefunction or functions noted in the blocks may occur out of the ordernoted in the figures. For example, in some cases, two blocks shown insuccession may be executed substantially concurrently, or the blocks maysometimes be performed in the reverse order, depending upon thefunctionality involved. Also, other blocks may be added in addition tothe illustrated blocks in a flowchart or block diagram.

Thus, the illustrative embodiments provide a low-energy computing systemthat may be used to implement a sequence of computers. Each computer maycomprise an adiabatic memory with a high percentage of energy recyclingand a processor with low energy signals. Each core of the processor usesan error correction code to detect errors arising due to the low energysignals and other factors. An address connection from the processor tothe memory includes validation of the address using a residueinteracting function block and conversion of the low energy signals intohigher energy signals.

Each future generation of this computing architecture may have adiabaticmemories with higher percentages of energy recycling and processors withlower energy signals. In this manner, energy efficiency may be increasedby using more sophisticated circuit components and error correctioncodes without sacrificing performance.

The description of the different illustrative embodiments has beenpresented for purposes of illustration and description, and is notintended to be exhaustive or limited to the embodiments in the formdisclosed. Many modifications and variations will be apparent to thoseof ordinary skill in the art. Further, different illustrativeembodiments may provide different features as compared to otherdesirable embodiments. The embodiment or embodiments selected are chosenand described in order to best explain the principles of theembodiments, the practical application, and to enable others of ordinaryskill in the art to understand the disclosure for various embodimentswith various modifications as are suited to the particular usecontemplated.

What is claimed is:
 1. A method for managing access to a memory of acomputing system, the method comprising: transforming, by a controller,a plurality of operations that represent a computing job into anoperational memory layout that reduces a size of a selected portion ofthe memory that needs to be accessed to perform the computing job;storing, by the controller, the operational memory layout in a pluralityof memory cells within the selected portion of the memory; andcontrolling, by the controller, a sequence by which a processor in thecomputing system accesses the memory to perform the computing job usingthe operational memory layout, wherein the operational memory layoutreduces an amount of energy consumed by the processor to perform thecomputing job.
 2. The method of claim 1 further comprising: accessing,by the processor, a selected group of memory rows in the memoryaccording to the sequence determined by the controller, wherein theoperational memory layout spans a plurality of memory rows in the memorythat are included in the selected group of memory rows.
 3. The method ofclaim 1 further comprising: generating, by the controller, an initiallayout for the plurality of operations using sparse matrix theory. 4.The method of claim 3, wherein generating, by the controller, theinitial layout comprises: expressing, by the controller, the computingjob using a plurality of sparse matrix operations and a set ofadditional operations, wherein the plurality of sparse matrix operationscorrespond to a selected sparse matrix; and generating, by thecontroller, the initial layout that includes a representation of theselected sparse matrix.
 5. The method of claim 4, wherein transforming,by the controller, the plurality of operations that represent thecomputing job into the operational memory layout comprises:transforming, by the controller, the initial layout into the operationalmemory layout such that the operational memory layout is smaller in sizethan the initial layout.
 6. The method of claim 5, wherein transforming,by the controller, the initial layout into the operational memory layoutcomprises: converting, by the controller, the initial layout into theoperational memory layout using a graphing algorithm that minimizes anumber of rows in the operational memory layout and sets a number ofcolumns in the operational memory layout to equal a number of processorcores in the processor.
 7. The method of claim 1 further comprising:accessing, by the processor, each memory row in the selected portion ofthe memory consecutively according to the sequence; and implementing, bythe processor, a set of tasks corresponding to the each memory row inthe selected portion of the memory accessed to produce an output vectorthat is stored in the processor.
 8. The method of claim 1 furthercomprising: loading, by the controller, an input vector into a set ofprocessor cores that form the processor.
 9. The method of claim 1further comprising: loading, by the controller, a set of instructioncode definitions into the processor of the computing system, wherein amemory cell in the plurality of memory cells in the memory includes aninstruction code that is defined by a corresponding instruction codedefinition of the set of instruction code definitions.
 10. The method ofclaim 1, wherein transforming, by the controller, the plurality ofoperations that represent the computing job into the operational memorylayout comprises: transforming, by the controller, the plurality ofoperations into a plurality of nodes, wherein the plurality of nodesinclude a set of input nodes, a set of matrix element nodes, and a setof output nodes; and arranging, by the controller, the set of inputnodes, the set of matrix nodes, and the set of output nodes in atwo-dimensional layout for use in storing the set of matrix nodes in theplurality of memory cells in the selected portion of the memory.
 11. Themethod of claim 10 further comprising: storing, by the controller, theset of input nodes and the set of output nodes in registers associatedwith the processor in the computing system.
 12. The method of claim 1,wherein controlling, by the controller, the sequence by which theprocessor in the computing system accesses the memory comprises:controlling, by the controller, a switch system such that the switchsystem electrically connects a selected group of memory rows in thememory according to the sequence, wherein the switch system enables abi-directional flow of energy between an energy storage unit and thememory.
 13. An apparatus comprising: a memory; a processor; and acontroller in communication with both the memory and the processor,wherein the controller transforms a plurality of operations thatrepresent a computing job into an operational memory layout that reducesa size of a selected portion of the memory that needs to be accessed toperform the computing job; stores the operational memory layout in aplurality of memory cells within the selected portion of the memory; andcontrols a sequence by which the processor accesses the memory toperform the computing job using the operational memory layout, whereinthe operational memory layout reduces an amount of energy consumed bythe processor to perform the computing job.
 14. The apparatus of claim13, wherein the processor accesses a selected group of memory rows inthe memory according to the sequence determined by the controller,wherein the operational memory layout spans a plurality of memory rowsin the memory that are included in the selected group of memory rows.15. The apparatus of claim 13, wherein the controller generates aninitial layout for the plurality of operations using sparse matrixtheory.
 16. The apparatus of claim 15, wherein the controller expressesthe computing job using a plurality of sparse matrix operations and aset of additional operations, and wherein the plurality of sparse matrixoperations correspond to a selected sparse matrix.
 17. The apparatus ofclaim 16, wherein the controller generates the initial layout thatincludes a representation of the selected sparse matrix and wherein thecontroller transforms the initial layout into the operational memorylayout such that the operational memory layout is smaller in size thanthe initial layout.
 18. The apparatus of claim 17, wherein thecontroller transforms the initial layout into the operational memorylayout using a graph layout algorithm that minimizes a number of rows inthe operational memory layout and sets a number of columns in theoperational memory layout to equal a number of processor cores in theprocessor.
 19. The apparatus of claim 13, wherein the operational memorylayout comprises: a plurality of nodes in which each node comprises atleast one of a numerical value or an instruction code.
 20. The apparatusof claim 13 further comprising: a switch system, wherein the controllercontrols which memory row of the memory the switch system electricallyconnects to, and wherein the switch system enables a bi-directional flowof energy between an energy storage unit and the memory.
 21. A methodfor managing access to an adiabatic memory circuit, the methodcomprising: transforming, by a controller, a plurality of operationsthat represent a computing job into an operational memory layout thatreduces a size of a selected portion of a memory array in the adiabaticmemory circuit that needs to be accessed to perform the computing job;storing, by the controller, the operational memory layout in a pluralityof memory cells within the selected portion of the memory array; andcontrolling, by the controller, a sequence by which a processor in acomputing system accesses the memory array in the adiabatic memorycircuit to perform the computing job using the operational memorylayout, wherein the operational memory layout reduces an amount ofenergy consumed by the processor to perform the computing job.